A slash chord is nothing more than a chord with an alternate bass note.
They're also called compound chords.
When you see a chord like A/E, the first character is the chord and the second character after the slash is the bass note, so A/E would be an A chord with an E bass note instead of an A bass note.
Some of the most common types of slash chords are inversion based, meaning that one of the notes already in the chord triad are used for the bass note.
G/B, D/F#, A/C#, A/E...all are inversions of the chord but using either the 3rd note of the 5th note as the bass note instead of the root note.
Some slash chords are non-inversion based, like B/E. The B triad is B, D#, F#...there's no E there BUT if you add extensions to the triad to make, say, a BMaj9/E, then you've got B, D# and F# as well as C# and E so BMaj9/E becomes inversion based.